Myths
Absolute Space
Points of View
Twin Paradox
Einstein's Train
Andromeda Paradox
Time in Spacetime
Clocks & Time
Velocity of Light
Einstein's Train
This version of the Einstein's Train scenario is taken from Wikipedia. It seeks to explain how differences in simultaneity arise. However, it does not go on to look at the consequences. I'd therefore like to firstly summarise the example as given, then expand it to consider the consequences.
The summary:
- A strobe light mounted in the middle of a railway carriage sends out a single pulse towards the front and the back of the carriage.
- To an observer on the train the ends of the carriage are an equal distance from the source of the light, and the light approaches both at the same speed. So the light reaches the front and the back of the carriage simultaneously.
- To an observer on the platform, the light is moving towards the back and front of the carriage at equal speeds, but because the carriage is moving, the back of the carriage is approaching the light, whilst the front is receding. So the light travelling to the back of the carriage has less distance to travel than the light travelling to the front. So the light reaches the back of the carriage before the front.
- Hence events which are simultaneous to the observer on the train are not simultaneous to the observer at the station.
That's a summary of the explanation given in Wikipedia, and it seems to suggest that the difference in simultaneity is a real, measurable, occurrence. However, we can extend the example to consider the consequences of this scenario, as follows...
Let us assume that when the light beams reach the end walls of the carriage, each triggers a beeper. There are two directional microphones co-located with the strobe light, such that if both receive a beep simultaneously, the the strobe flashes again. If the beeps are not received simultaneously, the strobe does not fire. So will the strobe light keep firing or not? Well, from the point of view of the passenger on the train:
- The light reaches each end of the carriage simultaneously, so the beepers sound simultaneously.
- The sounds travel at the same speed (relative to the carriage) so they reach the microphones simultaneously.
- So the strobe light keeps flashing.
Whereas, the situation is a little more complex from the point of view of the person on the platform:
- Because the light reaches the back of the carriage first, that beeper sounds first. You might therefore expect that the sound would reach the microphone first, but you'd be wrong.
- Because the two events (the sounds reaching the microphones) are co-located and simultaneous (from the point of view of the passenger on the train), we know that they are simultaneous in all frames of reference. So the sounds must reach the microphones together. But how can that be?
- The answer is that, because the speed of the sounds is the same in the frame of reference of the carriage, then the speeds will differ when viewed in the frame of reference of the platform.
- The difference in the speed of the sounds exactly counteracts the difference in when they were sounded. So the sounds arrive simultaneously, and the strobe light keeps flashing.
So although there appeared to be a difference in simultaneity when the beeps were emitted, when the sounds reach the microphones, the difference in simultaneity disappears. This leads us to question whether the difference in simultaneity is a real phenomenon? We pursue that question in the Two Towers example. However, we have some other myths to consider before we reach that one...
